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First-Principles Study of the Interactions Between GrapheneOxide and Amine-Functionalized Carbon Nanotube Sanjiv K. Jha, Michael Roth, Guido Todde, J. Paige Buchanan, Robert D Moser, Manoj K. Shukla, and Gopinath Subramanian J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 20 Dec 2017 Downloaded from http://pubs.acs.org on December 20, 2017

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The Journal of Physical Chemistry

First-Principles Study of the Interactions Between Graphene-Oxide and Amine-Functionalized Carbon Nanotube Sanjiv K. Jha,∗,† Michael Roth,‡ Guido Todde,‡ J. Paige Buchanan,¶ Robert D. Moser,¶ Manoj K. Shukla,§ and Gopinath Subramanian‡ †Department of Physics, Samford University, Birmingham, Alabama 35229, United States ‡School of Polymers and High Performance Materials, University of Southern Mississippi, Hattiesburg, Mississippi 39406, United States ¶US Army Corps of Engineers, Engineer Research and Development Center, Concrete and Materials Branch, 3909 Halls Ferry Road, Vicksburg, Mississippi 39180, United States §US Army Corps of Engineers, Engineer Research and Development Center, Environmental Laboratory, 3909 Halls Ferry Road, Vicksburg, Mississippi 39180, United States E-mail: [email protected]

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ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract We applied plane-wave density functional theory to study the effects of chemical functionalizations of graphene and carbon nanotube (CNT) on the properties of graphene + CNT complexes. The functionalizations of graphene and CNT were modeled by covalently attaching oxygen-containing groups and amines (NH2 ) respectively, to the surfaces of these carbon nanomaterials. Our results show that both dispersion energy and hydrogen bonding play crucial roles in the formation of complexes between graphene oxide (GO) and CNT−NH2 . At a lesser degree of functionalization, the interaction energies between functionalized graphene and CNT were, either unchanged or decreased, with respect to those without functionalization. Our study indicated that the gain or loss of interaction energy between graphene and CNT is a competition between two contributions: dispersion energy and hydrogen bonds. It was found that the heavy functionalization of graphene and CNT could be a promising route for enhancing the interaction energy between them. Specifically, the carboxyl functionalized GO produced the greatest increase in the hydrogen bond strength relative to the dispersion energy loss. The influence of Stone-Wales defects in CNT on the computed interaction energies were also examined. The computed electron density difference maps revealed that the enhancement in the interaction energy is due to the formation of several hydrogen bonds between oxygen-containing groups of GO and NH2 −groups of CNT. Our results show that Young’s moduli of carbon nanomaterials decrease with the increasing concentration of functional groups. The moduli of GO + CNT−NH2 complexes were found to be the averages of the moduli of their constituents.

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1

INTRODUCTION

In the world of nanotechnology, sp2 -hybridized carbon nanomaterials, such as graphene, 1,2 and carbon nanotubes (CNTs) 3 have attracted considerable attention. The remarkable electronic, 2 thermal, 4 and mechanical 5,6 properties of graphene and CNTs make them promising materials for a wide spectrum of applications, ranging from electronics to composites. 2,7–15 However, the low chemical reactivity and insolubility of pristine carbon nanomaterials limit the range of their potential applications, and emphasize the need for chemical modifications. Therefore, covalent functionalizations of carbon nanomaterials with various functional groups, such as hydrogen, 16 oxygen-containing groups, 17–20 amines, 21–26 and others, 27,28 have been studied, both experimentally and theoretically, as a route to improve the properties and expand the spectrum of their possible applications. 29–31 The functionalization of CNT not only improves its solubility in water and organic solvents, but also prevents the formation of CNT bundles. Graphene oxide (GO) consists of sp2 -hybridized carbon surface modified by oxygencontaining functional groups. 11,18,20,21,32–37 While, the oxygen content of GO could vary greatly, depending on the experimental conditions, 38 it is generally accepted that GO contains epoxy (>O), hydroxyl (–OH), and carboxyl (–COOH) functional groups. 11,21,32,34,37,39–41 The availability of the oxygen-containing functional groups makes GO readily soluble in aqueous media, 11 and expands the spectrum of its potential applications, in batteries, sensors, solar cells, supercapacitors, 36,42 and drug delivery. 43 Previous investigations on the interactions between graphene and CNT 44–48 have shown that graphene + CNT complexes possess superior properties over the individual carbon nanomaterials, such as enhanced stability, capacitance, electrical conductivity, and mechanical properties. 44–46 The computational study of Wang et al. 47 indicates that the interaction between graphene and CNT is mediated by weak van der Waals forces. Our recent density functional theory (DFT) investigation 48 on the interaction between graphene and CNT yielded the interaction energy of −1.61 eV/nm. Furthermore, graphene was able to promote 3



the dispersion of CNTs in the polymer matrix, resulting in the highest values of mechanical properties for nanocomposites containing graphene + CNT nanocarbon. 48 Therefore, understanding the nature and mechanism of graphene−CNT interactions provides a route for the synthesis of high performance nanocomposites. To achieve better performance of graphene + CNT complexes, it is desirable to optimize the interfacial interaction (binding) between graphene and CNT. One of the simplest routes to modify the interfacial interactions is thought to be the covalent functionalizations of these carbon nanomaterials with suitable chemical agents. Out of a limited number of available chemical agents, the oxygen-containing groups, 17–20 and amines, 21–26 have been extensively used for the functionalizations of graphene and CNT respectively. Therefore in the present study, we model functionalized graphene and CNT by attaching oxygen-containing groups and amines (NH2 ) respectively, to the surfaces of carbon nanomaterials. We hypothesize that such functionalizations would enhance the interaction energies between graphene and CNTs by forming hydrogen bonds. 21,49 Our goal is to explore the effects of chemical functionalizations of graphene and CNT on the properties of graphene + CNT complexes using DFT method.

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2

COMPUTATIONAL METHODS

Figure 1: Schematic of six different models of GO employed in our study. GOs were modeled by attaching (a) two epoxy groups (model I), (b) two hydroxyl + two carboxyl groups (model II), and (c) two epoxy + two hydroxyl + two carboxyl groups (model III), to the surface of graphene. GOs shown in (d)−(f) (models IV−VI) represented graphene sheets functionalized by four epoxy groups only, four hydroxyl groups only, and four carboxyl groups only, respectively. Atom colors scheme: C in gray, O in red, and H in white.

Plane-wave DFT calculations were performed using Quantum ESPRESSO (version 6.0) package 50 with the van der Waals functional (vdW-DF2). 51,52 The vdW-DF2 functional has been successfully used in describing the van der Waals forces in several previous studies. 53,54 Since the vdW interactions are very important in the current study, some test calculations using semi-empirical Grimme’s-D2 method 55 were also performed. The electron-ion interactions were treated with ultrasoft pseudopotentials 56 taken from the publicly available repository of the Quantum ESPRESSO distribution. The ultrasoft pseudopotentials avail-

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Figure 2: Geometries of NH2 –functionalized (a) pristine CNT, and (b) SW-defected CNT. Atom colors scheme: C in gray, N in blue, and H in white. able in the repository for the PBE (Perdew–Burke–Ernzerhof) functional were used in our calculations. The electronic states (Kohn-Sham wave functions) were expanded using the plane-wave basis sets with kinetic-energy cutoffs of 30 Ry and 240 Ry for the wave functions and charge densities, respectively. All atomic positions and lattice parameters were fully optimized using BFGS algorithm, until the components of Hellmann–Feynman forces acting on each atom were less than 10−3 Ry/Bohr, and the energies were converged to within 10−4 Ry in the self-consistent step. Due to the large system size (containing up to 298 atoms), only the Γ-point (k = 0) of the Brillouin zone was sampled. 57 The computed results were further verified using 2 × 2 × 1, and 3 × 3 × 1 k-points. 58 The infinite graphene sheet containing 112 carbon atoms was modeled using an or˚3 . GOs were modeled by thorhombic supercell with dimensions of 9.88 × 29.92 × 46.00 A covalently attaching oxygen-containing functional groups, such as epoxy (>O), hydroxyl (−OH), and carboxyl (−COOH), to the surface of graphene. 37 These functional groups were randomly distributed on the surface of graphene to represent a realistic model. 59 Different models of GO employed in our study are shown in Figure 1, where models I, II, and III represent graphene sheets functionalized with two epoxy groups, two hydroxyl + two carboxyl groups, and two epoxy + two hydroxyl + two carboxyl groups, respectively. To investigate which if any of the three oxygen groups produces the greatest effect in the interaction ener-

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Figure 3: (a)−(d) Geometries of heavily functionalized models of GO (models VII−X), and (e) NH2 –functionalized CNT. Heavily functionalized GO and CNT were were modeled using ten oxygen-containing groups and six NH2 −groups, respectively. gies, we further considered three more models of GO (models IV, V, and VI) with similar amounts of coverage, as shown in Figure 1d−f. These three models of GO (represented by IV, V, and VI in Figure 1) were obtained by functionalizing graphene sheets with four epoxy groups only, four hydroxyl groups only, and four carboxyl groups only, respectively. The armchair (8,8) CNT was modeled by a periodic supercell containing 128 carbon atoms. The Stone-Wales (SW) defects 60 in CNT were obtained by rotating a C–C bond by 90◦ about its center. The functionalizations of CNTs were modeled by covalently attaching two NH2 −groups to the sidewalls of pristine and SW–defected CNTs, as shown in Figure 2. The interactions between GO and CNT were studied by placing them in the same orthorhombic supercell. The equilibrium separation between GO and CNT was determined by minimizing the total energies and forces acting on all atoms. To investigate the effect of concentration of functional groups on the properties of complexes, the interactions between GO and CNT were examined using heavily functionalized models, as shown in Figure 3. The heavily functionalized models of GO were obtained using ten oxygen-containing groups,

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while that of the CNT was obtained using six amine groups. Four different models of GO displayed in Figure 3a−d (models VII−X) represented graphene sheets functionalized (heavily) with different combinations of oxygen-containing groups. Specifically, model VII represented graphene sheet functionalized with two epoxy + four hydroxyl + four carboxyl groups, model VIII represented the graphene functionalized with ten epoxy groups only, model IX represents the graphene functionalized with ten hydroxyl groups only, and model X represented the graphene functionalized with ten carboxyl groups only.

2.1

Interaction Energy Calculation

The interaction energy, Eint , between two species A and B was computed as,

Eint = EAB − EA/AB − EB/AB

(1)

where EAB represents the total energy of the complex AB, EA/AB is the total energy of species A within the geometry of the complex, and EB/AB is the total energy of species B within the geometry of the complex. With this definition, negative values of the interaction energies correspond to the stable configurations. All the computed interaction energies were normalized by the length of the CNT (cell dimension along x-direction). The interaction energy defined by equation (1) includes the deformations in the geometries of individual species due to complex formation. 61,62 Another way of obtaining the interaction energy involves the calculations of total energies of constituents in their own optimized positions. The difference in the interaction energies between these two methods gives the deformation energy, which is defined as the energy required for deforming the individual species from their separated minimum energy geometries to their distorted geometries in the optimized structure of the complex. 62

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2.2

Electron Density Difference Calculation

To understand the nature of the interaction during the complex formation, the electron density difference maps were examined. For a fully optimized configuration, the electron density difference was calculated by subtracting the electron densities of the individual species within the geometry of the complex, from the electron density of the whole complex as,

∆ρ = ρAB − ρA/AB − ρB/AB

(2)

where ρA and ρB represent the electron densities of species A and B within the geometry of the complex AB, and ρAB represents the electron density of the complex AB. The electron density difference maps were generated using the VESTA package. 63

2.3

Young’s Modulus Calculation

Young’s modulus is a physical quantity used to measure the strength of a material. The Young’s modulus was calculated using the second derivative of energy with respect to strain as, 1 ∂ 2E Y = V0 ∂ε2

(3)

where V0 is the equilibrium volume (volume of unstrained system), E is the total energy, and ε is the engineering strain. The volume of graphene was obtained using V0 = a × b × t, where a, b, and t represent length, width, and thickness respectively. The volume of CNT was calculated as the volume of a hollow cylinder using V0 = 2πrl0 t, where r, l0 , and t represent radius, equilibrium (relaxed) length, and thickness respectively. The radius, r of the CNT was calculated to be

10.98 2

◦

= 5.49 ˚ A. We have used t = 3.33 A, the equilibrium

separation between graphene and CNT, as a thickness for both graphene and CNT. 23,25 Similarly, for functional groups, the volume of atoms were obtained by treating them as spheres with radii equal to their van der Waals radii. To obtain the Young’s modulus, we

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performed total energy calculations for unstrained and strained structures. The energies of unstrained structures were obtained by the variable-cell relaxations. The energies of strained structures were obtained by applying small strains, ε = ±0.005 (±0.5%), and re-scaling the new coordinates of the atoms to fit within the new cell dimensions. After applying the strain, only atomic positions of the systems were re-optimized keeping the cell dimensions fixed. The value of curvature (i.e.,

∂2E ) ∂ε2

at the energy minimum (ε = 0) was obtained using

the central difference formula.

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3

RESULTS AND DISCUSSION

For pristine graphene and CNT, our plane-wave DFT calculations predicted an average ◦

equilibrium C–C bond length to be 1.42 A, that is consistent with previous experimental ◦

value of 1.42 A for graphite and graphene.

3.1

Interactions between Graphene-Oxide and Carbon Nanotube

Figure 4: Optimized geometries of complexes of model I of GO with (a) pristine CNT, (b) CNT−NH2 , (c) SW-defected CNT, and (d) SW-defected CNT−NH2 . GO was modeled by attaching two epoxy groups to the surface of graphene.

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Figure 5: Optimized geometries of complexes of model II of GO with (a) pristine CNT, (b) CNT−NH2 , (c) SW-defected CNT, and (d) SW-defected CNT−NH2 . GO was modeled by attaching two hydroxyl + two carboxyl groups to the surface of graphene.

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Figure 6: Optimized geometries of complexes of model III of GO with (a) pristine CNT, (b) CNT−NH2 , (c) SW-defected CNT, and (d) SW-defected CNT−NH2 . GO was modeled by attaching two epoxy + two hydroxyl + two carboxyl groups to the surface of graphene. Optimized geometries for various GO + CNT complexes are shown in Figures 4−6, where first three models of GO (models I−III) have been employed. These three models of GO were obtained by the functionalizations of graphene sheets with two epoxy groups, two hydroxyl + two carboxyl groups, and two epoxy + two hydroxyl + two carboxyl groups, respectively. The computed geometries of the complexes indicate that the covalent functionalizations of graphene and CNTs induce a significant deformation in their structures due to the local sp2 → sp3 transition of carbon atoms directly bonded to functional groups, that is consistent with the previous observations. 18,25,27 The computed interaction energies (per unit length of CNT) between first three models of GO and CNTs are summarized in Table 1. All computed interaction energies are negative, indicating that all the complexes are thermodynamically stable, and their formations are 13



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Table 1: Computed Interaction Energies and Equilibrium Separations between GO (Models I−III) and CNT

Eint (eV/nm)

dmin (˚ A)

a) GO + CNT (Pristine)

−1.66

3.38

b) GO + CNT−NH2

−1.08

4.56

c) GO + CNT (SW)

−1.56

3.22

d) GO + CNT (SW)−NH2

−1.03

5.07


−1.06

4.39

b) GO + CNT−NH2

−1.12

5.20

c) GO + CNT (SW)

−0.99

4.12


−1.27

5.47


−1.15

4.21

b) GO + CNT−NH2

−1.47

5.05

c) GO + CNT (SW)

−1.09

4.06


−1.54

5.31

Configurations Model I

Model II

Model III

energetically favorable. Table 1 shows that the interaction energy between model I of GO and pristine CNT (see Figure 4a) is −1.66 eV/nm, with the equilibrium separation (between C atoms of graphene ◦

and CNT) of 3.38 A. At this separation, the interaction between GO and CNT is governed by long range van der Waals forces. Comparing this result with the one obtained previously 48 for ◦

graphene−CNT interaction (i.e., Eint = −1.61 eV/nm, dmin = 3.33 A), we find that there is no significant change in the interaction energy or in the equilibrium separation between graphene and CNT due to the epoxy–functionalization of graphene. The presence of SW-defects in 14


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CNT produced a local deformation in it, however the interaction energy between GO and CNT was not significantly affected due to the defects (−1.66 eV/nm vs −1.56 eV/nm). This observation is qualitatively consistent with the previous theoretical result of Hassan et al., 64 where it was shown that the dispersion binding of a benzene on defected graphene is similar to the pristine one. Upon the functionalization of CNT with NH2 −groups (see Figure 4b), the interaction energy between GO and CNT was decreased to −1.08 eV/nm. Since the vdW interactions are very important in these systems, we further tested the suitability of the chosen vdW-DF2 correction method by recalculating the interaction energies between GO and CNT for a few selected configuration (Table 1, model I, systems a and b) using semi-empirical Grimme’s–D2 method. The interaction energies obtained from Grimme’s-D2 method agreed within 0.05 eV/nm to the value obtained from the vdW-DF2 method. A detailed comparison of the computed interaction energies using these two forms of the vdW corrections are provided in Table S1 of the Supporting Information. On examining the geometries of the complexes, the equilibrium separation between GO ◦

◦

and CNT was observed to increase from 3.38 A to 4.56 A due to the NH2 −functionalization of CNT, which in turn lowered the interaction energy significantly. The interaction energy between GO and CNT−NH2 is mainly due to the two contributions: dispersion energy and hydrogen bonding. By functionalizing the CNT with NH2 −groups, there is an energy gain due to the formation of hydrogen bonds between O of GO and NH2 of CNT; on the other hand, there is a loss of dispersion energy due to the increased separation between GO and CNT−NH2 . It appears that the dispersion energy played more dominant role than the hydrogen bonding in the present case, resulting in a decrease in the interaction energy due to the functionalization of CNT. In the present situation, there is one hydrogen bond formed between GO and CNT−NH2 (O· · ·NH, 2.15 ˚ A), while the other hydrogen bond is weak (O· · ·NH, 3.62 ˚ A). Thus, the NH2 −functionalization of CNT decreased the interaction energy between GO (model I) and CNT. Furthermore, the presence of SW-defects in CNT did not make a significant effect on the computed interaction energies.

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Figure 7: Computed electron density difference maps for the interactions of model I of GO with (a) pristine CNT, (b) CNT−NH2 , (c) SW-defected CNT, and (d) SW-defected CNT−NH2 . Yellow and cyan colors indicate gain and loss of electron density, respectively. Isosurface corresponds to 0.0008 e/bohr3 . The electron density difference maps for the interactions of GO (model I) with CNT are shown in Figure 7. In these plots, the isosurface in yellow (cyan) color indicates the region of electron gain (loss) due to the interaction. Since oxygen has a higher electronegativity than hydrogen, it pulls electron towards it. As seen in Figure 7b, the presence of a cyan region (electron loss) around the H atom, and a yellow region (electron gain) around the O atom indicates that the electron cloud migrates from the hydrogen towards the oxygen establishing the hydrogen bond.

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We next considered the interactions of model II of GO with CNT, which are shown in Figure 5. The interaction energy between GO and CNT is computed to be −1.06 eV/nm, ◦

with a separation of 4.39 A between them. Upon the NH2 −functionalization of CNT, the interaction energy increased slightly from −1.06 eV/nm to −1.12 eV/nm. At the same time, ◦

◦

the equilibrium separation between GO and CNT also increased from 4.39 A to 5.20 A. This indicated that the energy gained due to the formation of hydrogen bond is slightly higher than the dispersion energy loss due to the increased GO−CNT separation. Since the energy difference between two systems (Table 1, model II, systems a and b) that are being compared is very small (only 0.06 eV/nm), we re-computed the interaction energies using 2 × 2 × 1, and 3 × 3 × 1 k-points. Our results indicated that the interaction energies between GO and CNT obtained using denser k-points were converged within 0.01 eV/nm to that of the Γ-point. Our result confirmed that the observed small difference in interaction energy is not due to the lack of k-points. For the interested readers, the convergence of computed interaction energies between selected models of GO (models I and II) and CNT as a function of number of k-points is summarized in Table S2 of the Supporting Information. The interaction energy of GO with SW-defected CNT was computed to be −0.99 eV/nm, which was approximately same as that of GO with the pristine CNT. Furthermore, the interaction energy of GO with NH2 −functionalized SW-defected CNT was −1.27 eV/nm, which is somewhat higher than those of the remaining configurations shown in Figure 5 due to the shorter hydrogen bond distances (O· · ·HN, OH· · ·N). The NH2 −functionalization of CNT increased the number of hydrogen bonds, and consequently increased the interaction energy.

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Figure 8: Computed electron density difference maps for the interactions of model III of GO with (a) pristine CNT, (b) CNT−NH2 , (c) SW-defected CNT, and (d) SW-defected CNT−NH2 . Yellow and cyan colors indicate gain and loss of electron density, respectively. Isosurface corresponds to 0.0008 e/bohr3 . Optimized geometries for the complexes of model III of GO and CNT are shown in Figure 6. For the complex between GO and CNT (see Figure 6a), the interaction energy ◦

was computed to be −1.15 eV/nm, with a separation of 4.21 A between them. Upon the functionalization of CNT by NH2 –groups, the interaction energy between GO and CNT increased from −1.15 eV/nm to −1.47 eV/nm, and the equilibrium separation increased from ◦

◦

4.21 A to 5.05 A, which lowers the dispersion energy between them. The enhancement in the interaction energy between GO and CNT due to the NH2 –functionalization originated from the establishment of hydrogen bonds. Furthermore, we observe that the NH2 −functionalized SW-defected CNT interacts somewhat more strongly with GO (Eint = −1.54 eV/nm) due to the stronger hydrogen bond. However, the interaction energies between GO and CNT (or CNT−NH2 ) were always smaller (weaker) than that of the graphene−CNT interaction (Eint 18


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Table 2: Computed Interaction Energies and Equilibrium Separations between GO (Models IV−VI) and CNT. GOs were Modeled by Functionalizing Graphene Sheets with Four Epoxy Groups Only (Model IV), Four Hydroxyl Groups Only (Model V), and Four Carboxyl Groups Only (Model VI).

Eint (eV/nm)

dmin (˚ A)


−1.57

3.59

b) GO + CNT–NH2

−1.00

5.04


−1.03

4.37

b) GO + CNT–NH2

−1.18

5.11


−0.93

4.71

b) GO + CNT–NH2

−1.11

5.26

Configurations Model IV (>O)

Model V (−OH)

Model VI (−COOH)

= −1.61 eV/nm). The computed electron density difference maps shown in Figure 8 clearly indicate the interactions between GO and CNT. In order to know which if any of the three oxygen groups produces the greatest effect in the interaction energies, we further investigated the interaction of models IV−VI of GO with CNT. Optimized geometries for these interactions are provided in Figure S1 of the Supporting Information. We reiterate that these models of GO were obtained by functionalizing graphene sheets with only four epoxy groups, only four hydroxyl groups, and only four carboxyl groups, respectively. The computed interaction energies and equilibrium separations between GO and CNT are summarized in Table 2. The interaction energies between GO and CNT followed a similar trend as observed previously (for the interactions of models I−III of GO with CNT); that is the interaction energies between GO and CNT are, either unchanged (>O groups) or decreased (−OH, −COOH groups), with respect to that without 19



functionalizations (i.e., Eint = −1.61 eV/nm). Furthermore, NH2 −functionalization of CNT lowered the interaction energy in all the cases. This observation again suggested that the gain of interaction energy due to the hydrogen bonding was not sufficient to overcome the energy loss due to the dispersion. In summary, all the computed interaction energies between GO and CNT (and CNT– NH2 ) are, either approximately equal to or less than that of the graphene−CNT interaction (i.e., Eint = −1.61 eV/nm). 48 This suggests that the interaction energy between graphene and CNT can not be enhanced due to their gentle (light) functionalizations, which emphasizes the need for heavy functionalization, as a potential route for enhancing the interaction energy.

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Figure 9: Optimized geometries of complexes of model VII of GO with (a) pristine CNT, and (b) CNT−NH2 , where both graphene and CNT were heavily functionalized. GO was modeled by functionalizing graphene sheet with ten oxygen-containing groups (i.e., two epoxy + four hydroxyl + four carboxyl), while the functionalized CNT was modeled by using six NH2 −groups. Finally, we have investigated the influence of heavy functionalizations of graphene and CNT on their interaction energies. The heavily functionalized graphene and CNT are modeled using ten oxygen-containing functional groups and six NH2 −groups, respectively, as shown in Figure 3. As mentioned in the computational section 2, four different models of heavily functionalized graphene (see models VII−X, Figure 3) have been considered, and their interactions with CNT (and CNT–NH2 ) have been explored. As the presence of SWdefects in CNT did not make any significant change in the computed interaction energies between GO and CNT (as observed in Table 1, models I−III), therefore only the pristine model of CNT has been considered for the further study. Optimized geometries for the complexes of model VII of GO and CNT are shown in Figure 9, while those of models VIII−X of GO and CNT are provided in Figure S2 of the Supporting Information. The computed interaction energies between GO and CNT are summarized in Table 3. For model VII, we observe that the interaction energy between GO ◦

and CNT is −1.14 eV/nm, with a separation of 4.97 A. Upon the NH2 −functionalization of CNT, the interaction energy is increased to −2.11 eV/nm, that is almost double of the value obtained without the NH2 −functionlization. The functionalization of CNT also in21



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Table 3: Computed Interaction Energies and Equilibrium Separations between Heavily Functionalized Models of GO (Models VII−X) and CNT.

Eint (eV/nm)

dmin (˚ A)


−1.14

4.97

b) GO + CNT−NH2

−2.11

5.87


−1.70

4.02

b) GO + CNT–NH2

−1.42

5.28


− 1.23

4.40

b) GO + CNT–NH2

−1.90

5.22


−1.25

5.51

b) GO + CNT–NH2

−2.69

6.29

Configurations Model VII (>O, −OH, −COOH)

Model VIII (>O)

Model IX (−OH)

Model X (−COOH)

◦

◦

creased the separation between CNT and graphene from 4.97 A to 5.87 A. As discussed earlier, the increase in the GO–CNT separation due to the NH2 −functionalization resulted in lowering the dispersion energy. For models IX and X of GO, the computed interaction energies between GO and CNT followed a similar trend (as observed for model VII), where the NH2 −functionalization of CNT enhances the interaction energy between them. On the other hand for model VIII, the NH2 −functionalization of CNT lowered the interaction energies. Thus, except for the epoxy functionalized model, the interaction energies between heavily functionalized graphene and CNT were enhanced due to the NH2 −functionalization of CNT, which is essential for the development of high performance nanocomposites. Comparing the results of heavily functionalized models, we found that carboxyl functional groups produce 22


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the greatest increase in hydrogen bond strength relative to the dispersion energy loss. The computed electron density difference maps for the interactions between GO (model VII) and CNTs are shown in Figure 10. The NH2 –functionalization of CNT allowed the formation of a large number of hydrogen bonds between GO and CNT–NH2 , as revealed by the charge density difference map shown in Figure 10b. Since several hydrogen bonds are established, the energy gain due to the hydrogen bonds is much larger that the dispersion energy loss due to increased separation between GO and CNT. Thus the heavy functionalizations of graphene and CNTs resulted in a significant enhancement in the interfacial interaction energy, which is essential for the development of high performance nanocomposites. We reiterate that the interaction energies between GO and CNT reported in this manuscript were obtained using the total energies of constituents in the optimized geometries of their complexes. To investigate the effect of deformation on the computed interaction energies, we further evaluated the interaction energies for a few selected configurations using the total energies of the constituents in their own optimized position. A detailed comparison of the computed interaction energies using these two methods are provided in Table S3 of the Supporting Information. We observed that deformation corrected interaction energy is always higher than the other (obtained using constituents in their own optimized positions), and their difference represented the deformation energy, Edef . We further observed that the deformation energy is higher for the complexes forming hydrogen bonds.

23



Figure 10: Computed electron density difference maps for the interactions of model VII of GO (heavily functionalized graphene) with (a) pristine CNT, (b) CNT–NH2 . Yellow and cyan colors indicate gain and loss of electron density, respectively. Isosurface corresponds to 0.0008 e/bohr3 .

3.2

Elastic Properties

We consider here the effect of functionalizations on the Young’s moduli of graphene + CNT complexes. To validate our approach, we first computed the Young’s moduli of pristine structures. The simulated Young’s moduli of CNT and graphene were 1032 GPa, and 1068 GPa, respectively, which are consistent with the experimental values of ∼1000 GPa for CNT 6 and 1000 ± 100 GPa for graphene. 5 Our results are also in good agreement with the atomistic study of Milowska et al., 23 where the Young’s moduli of CNT and graphene are reported to be 1020 GPa, and 1050 GPa respectively. The computed Young’s moduli of various functionalized carbon nanomaterials are summarized in Table 4. It can be seen that the chemical functionalizations of CNT and graphene lower their mechanical strength. Due to the covalent functionalization, the hybridization of C atoms of CNTs (or graphene) changes from sp2 to sp3 ; which makes the functionalized structures softer than the pristine ones. The number of sp3 C atoms in CNT (or graphene) is directly associated with the number of functional groups, and therefore the modulus of CNT functionalized with six NH2 −groups is much lower than that with two NH2 −groups. 23 Similarly, the modulus of graphene is found to decrease with the increasing concentration

24


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Table 4: Simulated Young’s Moduli of Functionalized Carbon Nanomaterials

Configurations

Y (GPa)

CNT−2NH2 SW-CNT−2NH2 CNT−6NH2 model I GO model II GO model III GO model VII GO model I GO + CNT−2NH2 model II GO + CNT−2NH2 model III GO + CNT−2NH2 model VII GO + CNT−6NH2

967a 865b 834 1000c 881 845 645 986 927 887 749

a

YCNT = 1032, b YSW−CNT = 919, c YGraphene = 1068

of oxygen-containing functional groups, as shown in Table 4. The Young’s moduli of GO + CNT−NH2 complexes are found to be the averages of the moduli of their constituents.

25



4

CONCLUSIONS

We applied plane-wave density functional theory to investigate the effects of functionalizations of graphene and CNT on the properties of graphene + CNT complexes. The covalent functionalizations of graphene and CNT were carried out using oxygen-containing functional groups and amines, respectively. Our calculations showed that both dispersion energy and hydrogen bonding play crucial roles in the formation of complexes between GO and NH2 −functionalized CNT. The presence of SW-defects in CNT did not make any significant effect on the computed interaction energies. For a relatively lesser degree of functionalization of carbon nanomaterials, the computed interaction energies between functionalized graphene and CNT were, either unchanged or decreased, with respect to those without functionalization. It was observed that the gain or loss of interaction energy is a competition between two contributions: dispersion energy and hydrogen bonds. When the interaction energy gain from the hydrogen bonds is much larger than the interaction energy loss from the dispersion, there is a net gain in the interaction energy due to the functionalizations. Except for the epoxy functionalized model, the interaction energies between heavily functionalized graphene and CNT were enhanced due to the NH2 −functionalization of CNT. We observed that carboxyl groups of GO produced the greatest increase in hydrogen bond strength relative to the dispersion energy loss. Our simulations indicated that the functionalizations of graphene and CNT result in a loss of their mechanical strengths due to formation of weaker sp3 bonds. Young’s moduli of complexes of GO and CNT−NH2 were approximately the averages of the moduli of their individual constituent.

Supporting Information Available Table S1, Interaction energies between GO and CNT using vdW-DF2 and Grimme’s-D2 methods, Table S2, Interaction energies between GO and CNT as a function of number of k-points, Table S3, Interaction energies between GO and CNT obtained from the energies of 26


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constituents within the complex geometry, and within their own optimized geometry, Figures S1 and S2, Optimized geometries of complexes of GO and CNT. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The use of trade, product, or firm names in this report is for descriptive purposes only and does not imply endorsement by the U.S. Government. The tests described and the resulting data presented herein, unless otherwise noted, are based upon work partly supported by the U.S. Army Basic Research Program under PE 61102, Project T22, Task 01 “Military Engineering Basic Re-search”. Permission was granted by the Director, EL to publish this information. The findings of this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. S.K.J, M.R., G.T. and G.S. also acknowledge the startup funds from the University of Southern Mississippi. The authors acknowledge HPC at The University of Southern Mississippi supported by the National Science Foundation under the Major Research Instrumentation (MRI) program via Grant # ACI 1626217. High performance computing resources for this work were partly provided by the Mississippi Center for Supercomputing Research.

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